Problem: Eighty percent of adults drink coffee and seventy percent drink tea. What is the smallest possible percent of adults who drink both coffee and tea?
Solution: Adding together the percent of people who drink coffee with those who drink tea, we obtain a total of $150\%$.  Thus, we double-counted at least $50\%$, meaning that at least $\boxed{50\%}$ of adults drink both.  (The percentage who drink both ${\it can}$ be exactly ${50\%}$ if everybody drinks either coffee or tea; otherwise, the overlap is more than ${50\%}$, but the problem asked for the smallest possible overlap.)